Question

Is zero $(0)$ a real number?

Answer 1

o answer this question, you have to explain it with help of complex numbers and then divide the complex number into two branches that are real numbers and imaginary numbers then explain with the help of their respective criteria, if zero is a real number or an imaginary number.

Complete step by step solution:
In order to find out whether zero $(0)$ is a real number, we will first express it as a complex number, because each and every possible number (either real or imaginary) is a sub set of a complex number.
A complex number is expressed as a mixture of a real number and an imaginary number and also a complex number is represented by that is expressed as follows
$z = a + ib$
Where $a\;{\text{and}}\;b$ are real numbers and $i$ is the imaginary unit which is equal to $\sqrt { - 1}$ .
Now, in order to characterize it further, we will divide the complex number into two types:
I.Real numbers
II.Imaginary numbers
The complex number $z = a + ib$ will be real number if its imaginary part $(ib)$ equals zero, i.e. $b = 0$
Expressing zero $(0)$ as complex number, we will get
$0 = 0 + 0i$
From above, we can see that value of $b = 0$ , that means imaginary part of zero equals zero,
Therefore yes, zero $(0)$ is a real number.

Note : Each and every possible number in mathematics is a complex number, since the parent branch of all other number groups is a complex number, as there are two branches which are real numbers and imaginary numbers of complex numbers.